{"status": "success", "data": {"description_md": "When a student multiplied the number $66$ by the repeating decimal, \n$$\\underline{1}.\\underline{a} \\ \\underline{b} \\ \\underline{a} \\ \\underline{b}\\ldots=\\underline{1}.\\overline{\\underline{a} \\ \\underline{b}},$$ \n\nwhere $a$ and $b$ are digits, he did not notice the notation and just multiplied $66$ times $\\underline{1}.\\underline{a} \\ \\underline{b}.$ Later he found that his answer is $0.5$ less than the correct answer. What is the $2$-digit number $\\underline{a} \\ \\underline{b}?$\n\n$\\textbf{(A) }15 \\qquad \\textbf{(B) }30 \\qquad \\textbf{(C) }45 \\qquad \\textbf{(D) }60 \\qquad \\textbf{(E) }75$", "description_html": "<p>When a student multiplied the number <span class=\"katex--inline\">66</span> by the repeating decimal,<br/>&#10;<span class=\"katex--display\">\\underline{1}.\\underline{a} \\ \\underline{b} \\ \\underline{a} \\ \\underline{b}\\ldots=\\underline{1}.\\overline{\\underline{a} \\ \\underline{b}},</span></p>&#10;<p>where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are digits, he did not notice the notation and just multiplied <span class=\"katex--inline\">66</span> times <span class=\"katex--inline\">\\underline{1}.\\underline{a} \\ \\underline{b}.</span> Later he found that his answer is <span class=\"katex--inline\">0.5</span> less than the correct answer. What is the <span class=\"katex--inline\">2</span>-digit number <span class=\"katex--inline\">\\underline{a} \\ \\underline{b}?</span></p>&#10;<p><span class=\"katex--inline\">\\textbf{(A) }15 \\qquad \\textbf{(B) }30 \\qquad \\textbf{(C) }45 \\qquad \\textbf{(D) }60 \\qquad \\textbf{(E) }75</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "2021 AMC 10A Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc10A_p09", "prev": "/problem/21_amc10A_p07"}}